Preheat the oven to 200°C (400°F). Grease two ramekins with butter and dust them with cocoa powder.
Melt the dark chocolate and butter together until smooth. Let it cool slightly.
In a separate bowl, whisk together the powdered sugar, milk, and vanilla extract.
Add the melted chocolate mixture and mix until well combined.
Sift in the flour, cocoa powder, baking powder, and salt. Fold gently until a smooth batter forms.
Divide the batter evenly between the prepared ramekins, filling each about three-quarters full.
Bake for 10-12 minutes, until the edges are set but the center remains slightly soft.
Let the cakes rest for 1-2 minutes, then carefully invert onto serving plates.
Serve immediately with vanilla ice cream, fresh berries, or a dusting of powdered sugar.